20.13.1 problem 1

Internal problem ID [3810]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.1, page 587
Problem number : 1
Date solved : Monday, January 27, 2025 at 08:02:52 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 31

dsolve([diff(x__1(t),t)=2*x__1(t)+x__2(t),diff(x__2(t),t)=2*x__1(t)+3*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= 2 c_{1} {\mathrm e}^{4 t}-c_{2} {\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 67

DSolve[{D[x1[t],t]==2*x1[t]+x2[t],D[x2[t],t]==2*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{3} e^t \left (c_1 \left (e^{3 t}+2\right )+c_2 \left (e^{3 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{3} e^t \left (2 c_1 \left (e^{3 t}-1\right )+c_2 \left (2 e^{3 t}+1\right )\right ) \\ \end{align*}